Sports writer for The Age

Having made so much history already, the first Asian player to win a grand slam singles title now owns two. In her third Australian Open final, Li Na was not so much lucky as deserving; having carried the unfamiliar position of favouritism into the title bout on Rod Laver Arena, there was also, finally, a different result.

Li, 31, became the oldest Australian women's champion in the Open era by defeating Slovakian 20th seed Dominika Cibulkova 7-6 (7-3), 6-0 in 97 minutes, released to play freely after emerging from a tense first-set struggle to dominate the second.

A first-time champion was guaranteed, but Li's major breakthrough had come at the 2011 French Open, and one semi was as close as Cibulkova had previously been. For this next instalment, the world's third highest-paid female athlete pockets another $2.65 million and a first, priceless, Daphne Akhurst Memorial Cup, presented by Chris Evert.

When a Cibulkova forehand flew long on her second match point, Li raised her arms before an embrace at the net, and a beaming walk to her player box containing coach Carlos Rodriguez and husband Jiang Shan. Quite a subdued celebration, but just as Li had not lost her composure during tense moments in the first set, she did not overplay.

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''Finally, I get her,'' Li smiled, after briefly setting the trophy aside, then acknowledged her team, including her IMG agent Max Eisenbud who ''make me rich, thanks a lot'', Rodriguez, for believing in her and pushing her through the winter training that has so gloriously paid off. And, of course, Jiang, who ''gave up everything, just [to] travel with me, be my hitting partner, fix the drinks and fix the racquets. You are nice guy … and also you are so lucky [to] find me.''

Li had never lost to Cibulkova, but she had lost her two previous Melbourne Park finals, and almost in the third round of this one, when forced to save a match point against Lucie Safarova. In the Open era, only Serena Williams, Jennifer Capriati and Monica Seles have teetered as close to the precipice and survived to enjoy the view on finals night.

At a stretch: Dominika Cibulkova reaches for a backhand.

Last year, Li twisted her ankle in one fall and banged her head in another. There was an interruption for fireworks, and another ending with the runner's-up plate. No mishaps or missteps this time.

But it was also a marvellous tournament for the 161-centimetre Cibulkova, who had been told as a child that she should not play, could not, because she was too small to compete, and had beaten two top-five players en route to the biggest match of her life, but could not quite make it three. ''I don't really know where to start. It was just fantastic two weeks of my life and I think I gonna cry,'' she said as the tears flowed.

The 24-year-old first-timer had opened the more nervously, serving two double-faults in her first service game, the second on break point. Li, indeed, had two chances for a 3-0 lead, and the early signs were that the experienced Chinese competitor had settled best and quickest. But the Slovakian did not reach her maiden slam final by beating nobodies (refer Maria Sharapova, Agnieszka Radwanska et al), and nor, having come this far, was she about to beat herself.

After holding on for 2-1, she charged to the chair at a jog, loudly, and with intent. She levelled the terms at 3-3, but remained vulnerable on serve, saving one break point in the ninth game but finally conceding the second of the 11th.

Li's backhand is acknowledged as her superior groundstroke, but her forehand was horribly scratchy for a time, and her first serve percentage miserable, too, dipping below 30 per cent mid-set. Li served at 6-5, but was broken after missing a backhand down the line on set point.

Not since 2008 has an Australian Open women's final been played without one of the top three seeds; not since the all-Williams final of 2003 had there been a tie-breaker in a women's decider at Melbourne Park, and Li led it 5-1 and then 6-3 to earn her next set points, but needed only one.

Yet a sign that history was repeating, perhaps, for Li, was not necessarily a good thing, for the fourth seed had claimed the first set on the two previous occasions she had played the title match at Melbourne Park, only to lose both times - in 2011 to Kim Clijsters and last year to Victoria Azarenka. In the other 27 of the last 29 grand slam women's finals, the winner of the first set has won the match. This time, that would be Li.

She opened the second confidently, holding serve and then breaking again in the second game with the aid of another double-fault from Cibulkova and some improved footwork and forehand solidity of her own. By now, her confidence was growing, her forehand holding up better, her backhand still doing more of the damage in a winner count that finished 34 to 11. Indeed, the second set took just 27 minutes.

The oldest ever Australian Open women's champion is the first over-30 winner since Margaret Court claimed her 11th, in 1973, and the fourth seed will be reinstated to world No. 3 in the next WTA rankings list, while Cibulkova will exceed her previous high by rising to 13th.

Li admitted her life changed dramatically after she left Roland Garros in 2011, but expects that this time will be different. Just as, third time lucky, her attempt to win an Australian Open final proved to be.